Your posture is much better - but you're still shifting forward into the bar rather than pushing the bar back into yourself. Try doing some reps with an extremely slow first pull - 3 count or so - to upper thigh, then explode there while keeping your weight back and actively pushing the bar into your upper thighs with your lats. You're just in a bit of a hurry and you're starting your second pull way down at the knees - you have to wait much longer for it. Do that and you'll be far better balanced and quicker.

Quicker pull under. Your arms are a bit stiff during the pull and then your elbows come back instead of up and out as you start under the bar. Punch the legs and hips up together and immediately move the feet out and pull yourself down to the bar with the elbows high and out. That will keep you close to the bar and allow you to spin the elbows around as fast as possible. Otherwise, just getting your balance consistent.